At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To determine which of the given expressions are equivalent to [tex]\( x^{9/4} \)[/tex], we need to see if we can rewrite each expression to match [tex]\( x^{9/4} \)[/tex].
Let's analyze each expression step-by-step:
Expression A: [tex]\(\left(x^4\right)^{1 / 9}\)[/tex]
- Rewriting this expression using the power of a power rule [tex]\((a^m)^n = a^{mn}\)[/tex], we get:
[tex]\[ \left(x^4\right)^{1 / 9} = x^{4 \cdot (1 / 9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x}\)[/tex] as [tex]\( x^{1/4} \)[/tex], we get:
[tex]\[ (\sqrt[4]{x})^9 = (x^{1/4})^9 = x^{(1/4) \cdot 9} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression C: [tex]\(\sqrt[9]{x^4}\)[/tex]
- Rewriting [tex]\(\sqrt[9]{x^4}\)[/tex] as [tex]\( (x^4)^{1/9} \)[/tex], we get:
[tex]\[ \sqrt[9]{x^4}= (x^4)^{1/9} = x^{4 \cdot (1/9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x^9}\)[/tex] as [tex]\( (x^9)^{1/4} \)[/tex], we get:
[tex]\[ \sqrt[4]{x^9} = (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
- Rewriting [tex]\((x^9)^{1 / 4}\)[/tex] using the power of a power rule, we get:
[tex]\[ (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression F: [tex]\((\sqrt[3]{x})^4\)[/tex]
- Rewriting [tex]\(\sqrt[3]{x}\)[/tex] as [tex]\( x^{1/3} \)[/tex], we get:
[tex]\[ (\sqrt[3]{x})^4 = (x^{1/3})^4 = x^{(1/3) \cdot 4} = x^{4/3} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
So, the expressions that are equivalent to [tex]\( x^{9/4} \)[/tex] are:
- Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
Therefore, the correct answers are B, D, and E.
Let's analyze each expression step-by-step:
Expression A: [tex]\(\left(x^4\right)^{1 / 9}\)[/tex]
- Rewriting this expression using the power of a power rule [tex]\((a^m)^n = a^{mn}\)[/tex], we get:
[tex]\[ \left(x^4\right)^{1 / 9} = x^{4 \cdot (1 / 9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x}\)[/tex] as [tex]\( x^{1/4} \)[/tex], we get:
[tex]\[ (\sqrt[4]{x})^9 = (x^{1/4})^9 = x^{(1/4) \cdot 9} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression C: [tex]\(\sqrt[9]{x^4}\)[/tex]
- Rewriting [tex]\(\sqrt[9]{x^4}\)[/tex] as [tex]\( (x^4)^{1/9} \)[/tex], we get:
[tex]\[ \sqrt[9]{x^4}= (x^4)^{1/9} = x^{4 \cdot (1/9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x^9}\)[/tex] as [tex]\( (x^9)^{1/4} \)[/tex], we get:
[tex]\[ \sqrt[4]{x^9} = (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
- Rewriting [tex]\((x^9)^{1 / 4}\)[/tex] using the power of a power rule, we get:
[tex]\[ (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression F: [tex]\((\sqrt[3]{x})^4\)[/tex]
- Rewriting [tex]\(\sqrt[3]{x}\)[/tex] as [tex]\( x^{1/3} \)[/tex], we get:
[tex]\[ (\sqrt[3]{x})^4 = (x^{1/3})^4 = x^{(1/3) \cdot 4} = x^{4/3} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
So, the expressions that are equivalent to [tex]\( x^{9/4} \)[/tex] are:
- Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
Therefore, the correct answers are B, D, and E.
B and D and E
B = (c^1/4)^9 = x^9/4
D = (x^9*1/4) = x^9/4
E = (x^9)^1/4 = x^9/4
B = (c^1/4)^9 = x^9/4
D = (x^9*1/4) = x^9/4
E = (x^9)^1/4 = x^9/4
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.